Find one of those video montages of the many, many failures suffered by early rocketry programs everywhere. Without serious care they will. In short, that stuff is hard, man: it's rocket science.
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dmckee♦Sep 9 '12 at 1:51

2 Answers
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Nowadays, rockets use a Gimbaled Thrust System. The rocket nozzles are gimbaled (An appliance that allows an object such as a ship's compass, to remain horizontal even as its support tips) so they can vector the thrust to direct the rocket. In a gimbaled thrust system, the exhaust nozzle of the rocket can be swivelled from side to side. As the nozzle is moved, the direction of the thrust is changed relative to the center of gravity of the rocket.

Early rockets had Vernier Thrusters which uses small rocket engines on either sides, to control the altitude of a rocket. Nowadays, they are common in most satellites.

In this Image, The middle rocket shows the normal flight configuration in which the direction of thrust is along the center line of the rocket and through the center of gravity of the rocket. On the left one, the nozzle has been deflected to the left and the thrust line is now inclined to the center line at a gimbal angle $a$. As the thrust no longer passes through the center of gravity, a torque is generated about the center of gravity and the nose of the rocket turns to the left. If the nozzle is gimbaled back along the center line, the rocket will move to the left. On the right one, the nozzle has been deflected to the right and the nose is moved to the right.

Wikipedia says,

In spacecraft propulsion, rocket engines are generally mounted on a pair of gimbals to allow a single engine to vector thrust about both the pitch and yaw axes; or sometimes just one axis is provided per engine. To control roll, twin engines with differential pitch or yaw control signals are used to provide torque about the vehicle's roll axis.

The right & left gimbaling is necessary to direct the rocket to its original path, thereby maintaining its stability... This link gives a good explanation regarding the stability of rockets. This essay is also good, but it's somewhat big...

Another possible source of confusion is the misconception that gravity will pull a rocket over, due to thinking it is "supported" against gravity by the engines at its base. Gravity (apart from very weak tidal forces) acts on the rocket as a whole, not applying any torque. en.wikipedia.org/wiki/Pendulum_rocket_fallacy
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Christopher James HuffDec 30 '12 at 5:23

More fundamental than the gimballed thrust system or verniers is the relationship between the "center of gravity" and "center of pressure" on a rocket (or any kind of projectile (e.g., bullet).

For the rocket to fly nose-forward and not flip around, the center of gravity must be ahead of the center of pressure. In building small amateur or model rockets, the guideline is always that the CG should be at least 1 body diameter ahead of the CP.

The center of gravity is the point where the mass components of the rocket "act" with respect to the ground (i.e., you can treat the CG as a point representing "the rocket" when calculating the opposing force of gravity pulling the rocket downward). The center of pressure is the point where aerodynamic forces on the rocket body, nose, and any fins sum together and "act".

In the above answer about gimballed thrust, for example, the gimbals are actually acting to force the CP back under the CG when the nose tilts. Fins (e.g., on missiles or model rockets) act in the same way to keep the CP under the CG.

So individual technologies for doing that may vary, but the underlying principle here is the CG/CP relationship. Hope that helps.

That's fine for model rockets, but orbital launchers rapidly leave the atmosphere. CP is only relevant for the first minute or so of launch...and isn't relevant at all for launches from airless bodies. The answer is simply that they're actively stabilized, against both aerodynamic forces when present and any other small imbalances and misalignments in thrust. For an extreme example, a recent Falcon 9 launch lost one engine on the way up, along with an aerodynamic cover for the engine, but the guidance system was able to compensate.
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Christopher James HuffDec 30 '12 at 5:16

In buoyancy problems, the CP is necessarily under the CG, but those don't lead to unstable solutions. Instead, the CP moves to the side as the vessel tilts, and the question of stability is whether it moves horizontally further or less than the CG. In the case of a rocket, it's plainly obvious that the CP moves if the rocket tilts. The literal question of stability is if the CG-CP line rotates opposite the orientation of the rocket.
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Alan RomingerFeb 19 '13 at 15:56